I just did a quick tally (and anyone feel free to correct me) and this is what I came up with:
(Red) Security personnel: 19
(Red) Support Services: 8
(Blue) Sciences: 3
(Gold) Command: 7
That's the total for the series with the bulk of those happening in the second season. Of those 37 casualties 27 of them are redshirts and 8 of those are Engineering or Support Services. Overall casualties averaged over 3 years = 12.3 deaths per year.
Also, along with "Obsession" and "The Changeling", I would add "The Apple" as a major redshirt killer.
I'd say this is the reason the feeling that redshirts are doomed really persists. It's not just that they're the ones who die. It's that, in some episodes, they're the only
ones who die (The Apple just takes this to a ridiculous straining of probability), and this strains credulity.